Simulations were also carried out to compare the success rates of the PGROTP algorithm in sparse vector reconstruction with several existing algorithms, such as \(\ell _1\) -minimization, subspace pursuit (SP), orthogonal matching pursuit (OMP) and ROTP2 (in [1]}, [2]}).
The size of the measurement matrix is still \({500 \times 1000}\) .
For every given ratio of the sparsity level \(k\)  and \(n\) , the success rate of the algorithm is obtained by 50 random attempts.
In this experiment, SP, ROTP2 and PGROTP perform a total of 50 iterations, whereas OMP is performed \(k\)  iterations.
After performing the required number of iterations, the algorithm is counted as success if the condition (REF ) is satisfied.
The success rates for accurate and inaccurate measurements are summarized in Fig. REF  (a) and (b), respectively.
The inaccurate measurements are given as \(y=Ax^*+0.001\eta \) , where \(\eta \)  is a standard Gaussian vector.
Compared with several existing algorithms, it can be seen that the PGROTP is robust and efficient for the sparse vector reconstruction in both noise and noiseless environment.
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